In this paper, an error compensation technique for a dead reckoning (DR) system using a magnetic compass module is proposed. The magnetic compass-based azimuth may include a bias that varies with location due to the surrounding magnetic sources. In this paper, the DR system is integrated with a Global Positioning System (GPS) receiver using a finite impulse response (FIR) filter to reduce errors. This filter can estimate the varying bias more effectively than the conventional Kalman filter, which has an infinite impulse response structure. Moreover, the conventional receding horizon Kalman FIR (RHKF) filter is modified for application in nonlinear systems and to compensate the drawbacks of the RHKF filter. The modified RHKF filter is a novel RHKF filter scheme for nonlinear dynamics. The inverse covariance form of the linearized Kalman filter is combined with a receding horizon FIR strategy. This filter is then combined with an extended Kalman filter to enhance the convergence characteristics of the FIR filter. Also, the receding interval is extended to reduce the computational burden. The performance of the proposed DR/GPS integrated system using the modified RHKF filter is evaluated through simulation.